it is interesting i could not find many particle-particle simulators that simulate electrical fields even thought dynamics is pretty similar to that of planetary orbitals. there are few i could find but they are mostly 2D and defining problem in mathematical/geometrical terms, with sin/cos or some harmonic oscillator functions. none, however, i could find that simulate CLASSICAL ELECTRODYNAMICS (Stochastic El.Dynm. - SED) in 3D n-body system and even less to include MAGNETIC FIELDS, which are the effect of moving electric fields, says Lorentz and friends...

what is the force behind covalent bond? what came first, chicken or egg?

Merovingian:

You see, there is only one constant. One universal. It is the only real truth - Causality. Action, reaction.

Cause and effect.

how wonderful, the mystery and essence of Life, Universe and Everything lies in contradiction - the cause that is an effect of itself. ah, beautiful self-emerging craziness... im talking about field forces here, magnetic and electric.

...are magnetic dipoles the essence of Life, Universe and Everything? these dipoles would then need to be infinitely divisible while retaining its original properties, including the Yin-Yang duality, which is also kind of holographic quality, fractalous smell it has.... but, what the hell does it all mean?

ehmm, would you not think infinity goes both ways? infinite microcosmos, as well as macrocosmos... did you really think humans are on some "bottom" of grand scale of dimensions? hahaha... it's funny because its true, but not in the spatial sense, size does not matter scale-wise.

well, if there is any meaning in this blabbering, then let it be that universe is ANALOG, rather then digital... so, these particle accelerators and search for the smallest indivisible "atom" from which everything is composed will always be futile and more and more expensive, until it causes black hole and doom us all. science is great!

...its like smashing a clock off the wall in a hope to figure out how it works, by looking at all the broken pieces flying around.

You may have mused in the past, why one of my ....., or my girlfriend's .... is smaller than the other? well, look at that photo above, CHIRALITY is built-in. this universe is rather quier, it pulls on one side more than on the other. breaking of the symmetry...

in essence, i hope to be able to manage and somehow force these virtual atoms to aggregate with the use of "covalent bonds" by simulating it all with classical mechanics rather than quantum, which is contradictory to the "analog universe" somewhat....

I'm no expert on quantum mechanics, but from what I know about covalent bonds, they can be pretty reasonably modeled as springs between atoms. This actually captures a fair amount of molecular behavior.

Simulating atoms and molecules accurately using classical electrodynamics is pretty much impossible, as their interactions are determined by electron structure, which is totally quantum on atomic scales. In fact it was the massive problems encountered trying to apply electrodynamics to electrons in atoms that led to the development of quantum mechanics in the first place.

Your post is kind of vague and has several different concepts in it, as well as a lot of extraneous unrelated stuff. Can you condense it a bit and be more specific about what you're trying to do?

Your post is kind of vague and has several different concepts in it, as well as a lot of extraneous unrelated stuff. Can you condense it a bit and be more specific about what you're trying to do?

im sorry, i was blabbering a bit, but you got the essence of it - covalent bonding

I'm no expert on quantum mechanics, but from what I know about covalent bonds, they can be pretty reasonably modeled as springs between atoms. This actually captures a fair amount of molecular behavior.

quantum mechanics boils down to geometry, which is a way to avoid speaking of forces. i can not disagree with you because most of all i know about it comes from text-books, Wikipedia and what other people told us based on their research.

Simulating atoms and molecules accurately using classical electrodynamics is pretty much impossible, as their interactions are determined by electron structure, which is totally quantum on atomic scales. In fact it was the massive problems encountered trying to apply electrodynamics to electrons in atoms that led to the development of quantum mechanics in the first place.

well, i agree that it seems so, but we can actually use this CLASSICAL mechanics for pretty much everything else except for electron orbits. electric attraction/repulsion is _the force for most other molecular interactions. we even calculate subtle changes of angles in molecules due to electron repulsion.

interestingly, i can not find any mention of MAGNETIC FIELDS in regards to chemical bonding, all they talk about is attraction/repulsion between CHARGES aka electric fields. i suppose magnetic fields could be ignored in chemical bonding?

in any case, this is indeed very, if not the most, complicated subject, so let me again boil it down to simple question:

2.) what makes two neutral hydrogen atom attract in a first place?

...it will ultimately lead to Cooper electron pairing and Pauli exclusion principle which are only rules based on indirect observation.... on the other hand, there are papers and research seem to show that classical approach can give the same results/predictions as quantum uncertainty. thought, they mostly do this with balancing 'electrical radiation', or something along those lines.

the point is, i can not find if anyone has tried to do it this way - as 3D n-body simulation taking both MAGNETIC and ELECTRIC fields into account - so, id like some links about it, and if there are none, then i must conclude this is a first such try, huh?

Covalent bonds are created by the electromagnetic force (but you knew that already). But (as I understand it), we can't really understand this classically, as the negative electron clouds of two nearby atoms should always repel each other, according to classical physics. (In fact the whole notion of an electron cloud is unexplainable by classical physics.) Instead we have to understand it quantum-mechanically as a bound state of electrons in the potential well of two nearby nuclei, which has a lower energy and is therefore more stable than for two separated nuclei.

That being said, as you mentioned we don't really need the full formalism of QM to model covalent bonds unless we need to be really, really accurate. "Semiclassical" approaches that model the bonds as classical systems with a few additional assumptions (e.g. spring systems as I suggested, and perhaps the radiation-balancing approach you mention, though I don't know anything about it) can be pretty useful in practice. What does *not* work, however, is getting covalent bonds by simulating individual electrons using (unmodified) classical electrodynamics.

I'm not quite clear on what kind of N-body simulation you want to create

are you talking about modeling each atom as a body, with some kind of ad-hoc model for bonds, but abstracting away individual electrons? That sounds very doable, and I bet things like protein folding simulations use a technique like that. Are you talking about modeling each atomic nucleus and each electron as a body? That sounds to me like it would really run headlong into the brick wall of "QM != classical".

Instead we have to understand it quantum-mechanically as a bound state of electrons in the potential well of two nearby nuclei, which has a lower energy and is therefore more stable than for two separated nuclei.

i suppose my problem is that i can not accept that, i see no logic there - it just doesn't sound as explanation for anything. is that supposed to be based on laws of thermodynamics? electromagnetic force, as we know it, just does not explain it. where this energy potential came from? electric attraction/repulsion potential or some magnetic field potential?

electromagnetic force does not exist in quantum mechanics, but i do agree with you that we are nevertheless supposed to accept it is all due to electromagnetic force, which makes it contradictory for me - quantum theory positions two electrons in H2 molecule right next to each other, in between two protons.

it is almost a question of semantics - if electrons can merge or "pair-up", than they somehow got attracted to each other, which then breaks the very definition of repulsion between like charges.

I'm not quite clear on what kind of N-body simulation you want to create

i want to simulate 4 particles.

2 protons and 2 electrons. when i run this simulation i want to see 2 hydrogen atoms form spontaneously, just like on those YouTube videos. and then, i want to see them make covalent bond that will overcome general electric repulsion between electrons and protons.

Sorry that I cannot offer a better explanation, but the fact of the matter is that QM behaves in a way that is totally contrary to our intuition. Unfortunately, it just isn't easy to think about or visualize

you have to learn a whole new set of rules.

As for the simulations of two hydrogen atoms bonding, you can do that, but you have to be aware that for this purpose you CANNOT simulate the electrons as little point-particles that fly around and have a specific location and velocity. You just won't get a covalent bond out of that sort of simulation no matter what you do. In QM the electrons have a distributed nature, where their wave function is nonzero over a large region of space surrounding and connecting the two nuclei, and they do NOT have any specific location. So if you're interested in simulating electrons in a covalent bond you'll have to simulate their wave functions. Unfortunately I don't know any more details about this than what I've already said.

Then I guess my advice to you is to go learn quantum mechanics. Sorry that I cannot offer a better explanation, but the fact of the matter is that QM behaves in a way that is totally contrary to our intuition. Unfortunately, it just isn't easy to think about or visualize - you have to learn a whole new set of rules.

yes, but i already know QM, the trouble with it is that is not an explanation, nor is suitable for experimentation. but also, im trying to do something that has not been tried yet.

As for the simulations of two hydrogen atoms bonding, you can do that, but you have to be aware that for this purpose you CANNOT simulate the electrons as little point-particles that fly around and have a specific location and velocity.

iam talking about 3D N-body simulation with both MAGNETIC and ELECTRIC fields. are you saying that you know of similar attempts that failed, can you point some links?

i think you are not realizing that this particular approach has actually never been considered yet. originally, classical mechanics approach was discarded at the time mostly due to complexity of the simulation.

n-body system is chaotic, it is unpredictable as much as quantum mechanics is uncertain. we can not really know if it will work or not until we try it, we have no other means to predict it but it step by step...

there are current classical methods that actually CAN DO as good QM, that is what i read on the WWW. this is not new nor against mainstream, it is just not known due to great popularity of QM.

yes, but i already know QM, the trouble with it is that is not an explanation, nor is suitable for experimentation.

I'm not sure what you mean by this, but QM does give you the ability to calculate the properties of the hydrogen molecule very accurately, and those properties can be (and have been) tested by experiment. If you're saying it's "not an explanation" because the interpretation of what the wave function physically means isn't clear, that's fair enough, but I don't think it's a very good reason to ignore QM entirely, as you seem to want to do.@PlayStationX

iam talking about 3D N-body simulation with both MAGNETIC and ELECTRIC fields. are you saying that you know of similar attempts that failed, can you point some links?

I don't know of any specific cases I can point to where someone has attempted this, but I'm not a physicist.@PlayStationX

originally, classical mechanics approach was discarded at the time mostly due to complexity of the simulation.

I don't think that's true. If you consider a single atom all by itself, classical mechanics predicts the electrons will constantly lose energy and collapse into the nucleus. Since this is a two-body problem it's analytically solvable but it utterly fails to explain the stability of real atoms. This is one of the main facts that motivated physicists to develop QM. It had nothing to do with being unable to perform complex simulations.@PlayStationX

n-body system is chaotic, it is unpredictable as much as quantum mechanics is uncertain. we can not really know if it will work or not until we try it, we have no other means to predict it but it step by step...

That's true enough. If you think making this simulation is worthwhile, go ahead...but I stand by my earlier statement, that I do not believe it's possible to obtain a stable covalent bond from classical electrodynamics.@PlayStationX

there are current classical methods that actually CAN DO as good QM, that is what i read on the WWW. this is not new nor against mainstream, it is just not known due to great popularity of QM.

Can you post a link that explains what you're referring to? This sounds like it might be referring to one of the "semiclassical" approximations I mentioned earlier.

Edit: by the way, if you are interested in learning more details about QM, you might check out the Feynman Lectures on Physics, a three-volume set of introductory material on all branches of physics. The third volume is specifically about QM and includes treatment of the hydrogen molecule. (The link is for the whole set, but you can also get the individual volumes on Amazon. Or, if you don't want to buy a book, you can also check your local library.)

i need to explain and provide evidence that classical approach can indeed show some promising results....

Quote: Originally Posted by PlayStationX originally, classical mechanics approach was discarded at the time mostly due to complexity of the simulation.

I don't think that's true. If you consider a single atom all by itself, classical mechanics predicts the electrons will constantly lose energy and collapse into the nucleus. Since this is a two-body problem it's analytically solvable but it utterly fails to explain the stability of real atoms. This is one of the main facts that motivated physicists to develop QM. It had nothing to do with being unable to perform complex simulations.

yes, you are right. so my sentence came off not complete, not quite true.

the main reason for discard is what you say, but i was thinking of these other methods that have some theory of their own why electrons do not radiate or how they can gain energy back. so, let me correct - the computation complexity was the main reason to discard further analysis of classical approach of those methods and theories that somehow overcame the problem of "energy loss" due to "acceleration". i say what i read in papers - that interest in this approach is back since now computers can do much more.

there are few peculiarities with radiating electron:

1.) we say when light bends due to gravity - it does not accelerate, but "follows the curvature" of space-time, is this - QM or CM? ...when electron is moving with constant velocity, no matter how curved that path is, why do we not say it "follows the curvature", but we say it "accelerates" and therefore "radiates", what theory is this now - QM or CM?

2.) magnetic field is not quite conservative force. it acts perpendicular to velocity and distance vectors. magnetic field does not cause acceleration, even thought it causes charged particle to produce circular motion?! magnetic fields are velocity dependent, but what the hell is that velocity relative to - aether?

the second part, well, none of it makes any sense, its simply crazy. but, that is the best interpretation about magnetic fields i could produce from Wikipedia and the rest of the WWW.

so, my hopes and my main arguments will orbit around "magnetic fields"...

That's true enough. If you think making this simulation is worthwhile, go ahead...but I stand by my earlier statement, that I do not believe it's possible to obtain a stable covalent bond from classical electrodynamics. Can you post a link that explains what you're referring to? This sounds like it might be referring to one of the "semiclassical" approximations I mentioned earlier.

my theory is that when i include the "spin" of my charged particles, i would be able to model magnetic fields as strong as i wish, which could hopefully produce some overall attraction even between two electrons - if they're spinning fast enough and they are oriented the right way - then the magnetic attraction can maybe overcome electric repulsion and further lead to some aggregation and bonding.

i will collect some links, this is the main part of my argument so let me try to find something convincing...

links... these are not my arguments. "my theory" has to do with magnetic fields, but that might come to be the same as what these guys are talking about. these are the arguments to show classical approach can be used instead of QM:

Quantum Mechanical Ground State of Hydrogen Obtained from Classical Electrodynamics

The behavior of a classical charged point particle under the inﬂuence of only a Coulombic binding potential and classical electromagnetic zero-point radiation, is shown to agree closely with the probability density distribution of Schrödinger's wave equation for the ground state of hydrogen. These results again raise the possibility that the main tenets of stochastic electrodynamics (SED) are correct.

The following fact probably comes as a surprise to most physicists. A group of researchers in the past have both proposed and deeply investigated the idea that classical electrodynamics, namely, Maxwell's equations and the relativistic version of Newton's equation of motion, may describe much, if not all, of atomic physical processes, provided one takes into account the appropriate classical electromagnetic random radiation ﬁelds acting on classical charged particles. Stochastic electrodynamics (SED) is the usual name given for this physical theory...

Even though the Universe proves to be quantum mechanical at the microscopic level, classical electrodynamics is nevertheless extremely relevant and useful in the real world today at the macroscopic level. It describes extremely precisely nearly all the mundane aspects of ordinary electrical engineering and electromagnetic radiation from the static limit through optical frequencies.

Even at the molecular level or photonic level where it breaks down and a quantum theory must be used it is ﬁrst necessary to understand the classical theory before exploring the quantum theory, as the quantum theory is built on top of the entire relativistic electrodynamic conceptual framework already established.

ok, now i noticed that most of the papers i wanted to quote here are written by this guy - Daniel C. Cole. so if you search that name together with "SED" you can easily see the rest, but this is the essence of what i was referring to.

so, how does that sound?

anyway, all this still leaves the most important questions for me:

why is no one taking MAGNETIC FIELDS into account?

could it be that magnetic forces due to spin and velocity/direction actually can overcome electric repulsion of two electrons?

is magnetic force stronger than electric? how to compare the strength of magnetic and electric fields. it is hard to see where one ends and where the other begins. velocity and spin factors are confusing in these equations - we do not seem to know if magnetic field can influence motion of the particle itself...

my conclusion so far is this - magnetic fields are so mysterious and confusing that everybody wanted to forget about them, so much in fact that they invented QM just to run away from magnetism and other instantaneous forces, namely field forces.

magnetic fields are so mysterious and confusing that everybody wanted to forget about them

This is pure bullshit. Just google "quantum" and "magnetism" for an endless set of links to universities (small and unknown like Stanford) and groups (likewise small and unknown like NATO's Advanced Study Institute) that are researching this topic.

BTW, I studied quantum chemistry before getting into computers. I would highly recommend you take a university class on this, taught by a good physicist, if you are interested; it is perhaps the hardest subject matter I have ever encountered.

This is pure bullshit. Just google "quantum" and "magnetism" for an endless set of links to universities (small and unknown like Stanford) and groups (likewise small and unknown like NATO's Advanced Study Institute) that are researching this topic. BTW, I studied quantum chemistry before getting into computers. I would highly recommend you take a university class on this, taught by a good physicist, if you are interested; it is perhaps the hardest subject matter I have ever encountered.

you are very nice person. since you are educated, maybe you can be kind some more to actually argument your opinion? i do not even know what is your objection about, huh? anyway, what did they teach you, what is the force responsible for covalent bond?

now the interesting part, if you really have education in quantum chemistry then it only goes to prove my point since you demonstrated utter confusion about magnetic fields and everything else that you failed to understand by confusing it with "bullshit"

do you think you can actually articulate your opinion?

1.) magnetic field is not quite conservative force.

2.) magnetic field acts perpendicular to velocity and distance vectors.

3.) magnetic field does not cause acceleration, even thought it causes charged particle to produce circular motion?!

4.) magnetic field is velocity dependent, but what the hell is that velocity relative to - aether?

there you go, are you saying this is wrong or you're saying it is not confusing? well, pick anything, its all crazy... just please explain what exactly did you imagine is "bullshit"?

Wikipedia:

"Because the magnetic field is always perpendicular to the motion, the magnetic fields can do no work on a charged particle;

a magnetic field alone cannot speed up or slow down a charged particle. It can and does, however, change the particle's direction, even to the extent that a force applied in one direction can cause the particle to drift in a perpendicular direction..."

...it is perhaps the hardest subject matter I have ever encountered.

i believe you that. perhaps, if you were in my class you would know better.

but not to worry, here i am now, so feel free to ask and i will explain everything to you.

first, magnetism is an abstract term in QM as explained previously. so your suggestion to look for "quantum and magnetism" is quite ridiculous in itself, are you sure you studied quantum chemistry?

if you really have education in quantum chemistry then it only goes to prove my point since you demonstrated utter confusion about magnetic fields and everything else that you failed to understand by confusing it with "bullshit"

No. I am not confused at all. I am saying that your impression that everyone "runs away from magnetism" in the field of quantum physics is absolute BS, with hints of delusion and a medium paranoia aftertaste. It may be a language barrier, though.

There is a fair amount of work being done there but, like most quantum mechanics, it is still poorly understood because of its incredible complexity.

So, did you learn quantum theory from class or Wikipedia? Or, are you a physics professor? (Seems doubtful. You wouldn't be asking your question.) However, the two quotes appear contradictory...

Assuming the best-case scenario, and you are a professor, or student already in class and currently studying this, I recommend you walk down to your local university library and tap into the wonderful world of peer-reviewed physics journals, instead of expecting deep quantum theory discussion in a game development forum. Maybe they have a copy of "The Quantum Theory of Magnetism" if you need to start lower than physics and chemistry papers?

Now, if you want to discuss how to implement an gross approximation, or simplistic simulation of quantum forces at play (once you have your math down pat) that's another matter and unclear from your lengthy rambling...

No. I am not confused at all. I am saying that your impression that everyone "runs away from magnetism" in the field of quantum physics is absolute BS, with hints of delusion and a medium paranoia aftertaste. It may be a language barrier, though.

hahaha.. i see now, it was a joke.

did you really think i was literary saying they were running away? anyway, just a joke.. which is funny because its true.

So, did you learn quantum theory from class or Wikipedia? Or, are you a physics professor?

there is no OR, your logic is broken, it is all about AND operator.

i learned it in class AND from text-books AND also from Wikipedia AND also from WWW AND later i was again in a classroom, as a professor... and despite all that i still can learn something new everyday, because im not ignorant.

I recommend you walk down to your local university library and tap into the wonderful world of peer-reviewed physics journals...

why? what in the world are you talking about? i did quote you mainstream info from peer-reviewed journals, whats wrong with you?

Regarding statistical electrodynamics (which I did not know about before, so thanks for pointing it out), it is an interesting approach and I think worthy of some exploration, but the Wikipedia article suggests that there is also experimental evidence that agrees with QM and disagrees with SED. I can't see the actual paper it refers to, so I can't begin to evaluate this evidence. Anyway, it would be interesting to see what SED has to say about covalent bonds, if you are up to the task of building a simulator for it.

Nothing. I'm not complaining. I'm just saying that a) some of your initial assertions are false, and this is likely the wrong forum to ask questions on simulating covalent bonds... unless you want it to be purely illustrative. I was debunking and helping, a.k.a. "tough love", but you decided to take it the wrong way.

Here's the "nutshell": First, establish the model you want to represent, then come to developers on this forum and ask for help on how it can be modeled. This forum will probably not adequately answer your questions like "what makes two neutral hydrogen atom attract in a first place?". Presumably, you know more on that than many of us here...

Anyway, it would be interesting to see what SED has to say about covalent bonds, if you are up to the task of building a simulator for it.

i never heard about SED either, until just recently. i too would like to know if this method can cope with covalent bonds. i suppose i could simulate it if i had equations of motion for it, which i cant quite figure out. thought, they too seem to be forgetting about magnetic force, so it is not really what im after right now.

speaking of it, do you know of some source code or some SIMPLE and free-to-download software that can simulate H2 covalent bonding with QM(or anything), but in 3D and in real-time?

alpha,

Nothing. I'm not complaining. I'm just saying that a) some of your initial assertions are false, and b) this is likely the wrong forum to ask questions on simulating covalent bonds... unless you want it to be purely illustrative. I was debunking and helping, a.k.a. "tough love", but you decided to take it the wrong way.

i do not mind complaining, thats cool, but if you do not point exactly what is wrong we can not really discuss it.

a.) great, but what assertions? why can you not articulate it, simply just quote what you consider false.

b.) my question is if you can help me find some links to software that deals with charges, but also with magnetic fields. i hoped it could be as easy as pointing about many different solar system software and source code for it.

Here's the "nutshell": First, establish the model you want to represent, then come to developers on this forum and ask for help on how it can be modeled. This forum will probably not adequately answer your questions like "what makes two neutral hydrogen atom attract in a first place?". Presumably, you know more on that than many of us here...

you can do that when you do whatever you think those instructions are for. i think anyone past the high-school should be able to manage questions about covalent bonds and basic electromagnetic properties. and if not, then what a great opportunity to learn about it all and then use some of the crazy dynamics of electromagnets for the next-gen video game.

Anyway, it would be interesting to see what SED has to say about covalent bonds, if you are up to the task of building a simulator for it.

let me extend this same thought on QM, what does it say about covalent bonding and where can i find a simulation of it?

not modeling/drawing tool, but real-time simulation where i can see how two hydrogen atoms approach each other and how their electron clouds change and eventually form H2. is there software like this based on QM, real-time?

i think QM computations get pretty heavy as soon as you try to do anything but hydrogen bonding. i dont really know to what extent QM can be used for simulation of bonds, as opposed to visualization of orbits for which it is good but that does not involve any interaction.

1.) When two hydrogen atoms are at large distance from each other, there is no interaction between them. The total energy of the system is equal to the sum of the energies of the two H atoms.

2.) When the two atoms approach each other, electrons of one atom attract the nucleus of the other atom. Electrons of both the atoms are attracted by both the nuclei. These attractive interactions lead to a decrease in the energy. - NONSENSE

3.) When the two hydrogen atoms come still closer, the electron-electron and nucleus-nucleus repulsive interactions start operating. Repulsive interaction tends to increase the energy of the system. The energy of the system decreases as long as the attractive interactions are stronger than the repulsive interactions. At a certain distance there is a balance between the attractive and repulsive interaction and the system attains a minimum value. At this stage the two H atoms are at fixed distance and for m a stable H2 molecule. The inter-nuclear separation when the energy of the system is minimum is called bond length. - NONSENSE

-"The overlap of orbitals allows two electrons of opposite spin to share the common space between the nuclei, forming a covalent bond"

...well, that makes more sense, but it should be obvious that this changes the definition of repulsion between like charges... unless that "spin" property somehow can lead to attraction or "coupling". in any case this "SPIN factor" is very important...

now my theory should be easy to understand, it is only natural to compare these "opposite spins" of these electrons to the dipole nature of magnetic fields. in other words classical mechanics actually predicts two spinning electrons to attract if they spin in opposite directions. this seems rather obvious, but again - i do not see anyone mentioning any magnetic fields as a possible player in all this.

not modeling/drawing tool, but real-time simulation where i can see how two hydrogen atoms approach each other and how their electron clouds change and eventually form H2. is there software like this based on QM, real-time?

I don't know of any, but then again I'm not a physicist.

As alphadog says, you are really in the wrong forum for this kind of thing. Game developers never have a need to simulate QM in games, so we don't know much about it.

As for the bit about the electron spins, you are absolutely right that it is important. Two hydrogen atoms with the electron spins aligned cannot form a molecule; it only works if the electron spins are in opposite directions. QM explains this as due to the Pauli exclusion principle; the two electrons can't be in the same state. The graph of energy vs separation distance between the atoms looks very different for spins-parallel vs spins-antiparallel. BTW, the diagram on the tutorvista.com page you linked shows only the case for spins-antiparallel.

I think part of the problem is the websites you are citing are not really giving you the whole story; they are simplifying so as not to overwhelm the audience. You chould check out the Feynman Lectures I linked to earlier. The third volume includes a quantum-mechanical treatment of the hydrogen molecule that accounts for the electron spins. It also doesn't give you the whole story as it is for an introductory course, not an expert, but it gives you a lot more of the story.

I don't know of any, but then again I'm not a physicist. As alphadog says, you are really in the wrong forum for this kind of thing. Game developers never have a need to simulate QM in games, so we don't know much about it.

well, im talking about simple particle simulator with only 4 particles. i do not quite understand how can forum for master developers not be a good place to talk about this. there is plenty of stuff here about solar systems and planetary orbits.... all i was talking about is just as simple as that: F = m*a = Q1*Q2/r\\^2

what is a better place to discuss real-time particle simulation?

I think part of the problem is the websites you are citing are not really giving you the whole story; they are simplifying so as not to overwhelm the audience. You chould check out the Feynman Lectures I linked to earlier. The third volume includes a quantum-mechanical treatment of the hydrogen molecule that accounts for the electron spins. It also doesn't give you the whole story as it is for an introductory course, not an expert, but it gives you a lot more of the story.

im just simplifying and giving the first referrence that comes up on google search, but i am serious about it, so im referring to any and all available info. i like Feynman too, but he does not talk about real time simulation of magnetic forces. can you give a link to the part that might be relevant to this?